Does a high FG mean that the beer will be sweeter than a batch that
ferments down to 1.006 or lower?

I have read that a beer with a higher FG has more body, and a higher
level of unfermentable sugars, but I much prefer my beer "dry".

I have mostly used malt extract, both kits and unhopped. I've noticed
at my current house, over about five or six batches, that my FG is
always about 1.018. Fermentation had finished in all cases, and the
results have been anywhere from poor (shouldn't have used cane sugar in
that brew) to three or so good ones, to a couple I was very happy with.

I have very a high amount of iron in my tap water (just over 3 ppm)
although on the plus side, our water isn't treated in Christcurch, so no
chlorine or other chemicals.

According to Al Korzonas in his Homebrewing Vol. 1, Malt extracts tend
to have higher proportions of unfermentable sugars. I would suggest
if you want drier beer, that you get into all-grain brews, and that
you keep the mash temps at the lower end of the effective range. (148
- 160F). The higher end of this range will produce fuller body and
sweetness/the lower end more alcohol and less body & sweetness. It
might also help if you research the various liquid yeasts and choose
those rated High Attenuation. These will tend to ferment out more
completely.

For an extract brew, the makeup of your water is pretty much
unimportant...if it tastes good, it's fine for brewing. Some extracts
are less fermentable than others..Laaglander, for instance, is about 55%
fermentable. John Bull isn't much better. So one option is to change
to a more fermentable extract. Another option is to use a portion of
sugar in your beer. Not the heresy that some would have you believe.
Many extarcts (again, Laaglander is a prime example) are formulated to
be used with sugar. Sugar is 100% fermentable and adds no flavor to the
beer, so it will lighten and dry out your beers. Contrary to the old
wives tale, sugar does not cause cidery flavors in beer at amounts up to
about 20%. The cidery taste is cause by old, oxidized extract and sugar
adds no taste of its own to cover it. The old warnings about sugar were
based on using outdated kits. Other than those tiups, about the only
other way to control fermentability is to start brewing all grain. But
I think if you started maybe .5-1 lb. of sugar to your brews, you'd see
a marked improvement.

Another possibility for bringing the FG down would be a few beano
tablets (If they're not available in NZ, it's from GlaxoSmithKline -
www.beano.net. It claims that it's "Alpha-galactosidase enzyme
derived from Aspergillus niger - 150 GALU") in the wort. It breaks
down some of the unfermentables. I've heard that using enough of it
will bring the FG down below 1.000, but I've never tried to do that.

Actaully, using ANY of it can likely cause the FG to go that low. I've
experiemented wqith Beano several times. When I formulated the recipe
specifically to use it, the beer came out OK. Using it to "save" a beer
didn't produce very good results at all. You'd be much better off
finding the cause of the high FG and dealing with it at the source.